We can write our integral as:

`int(3\ dx)/(25+16x^2)=3int(dx)/((5)^2+(4x)^2`

For the formula, we need:

Re-arranging that last expression gives: `(du)/4=dx`.

We are now ready to perform the integration.

`int(3\ dx)/(25+16x^2)`

`=3/4int(du)/((5)^2+u^2)`

`=3/4xx1/5tan^-1 u/5+K`

`=3/20tan^-1 (4x)/5+K`

We could also write this answer as:

`3/20 arctan\ (4x)/5+K`